Xu Heng 許衡 (1209-1281), courtesy name Xu Zhongping 許仲平, style Luzhou xiansheng 魯齋先生, was a Confucian scholar of the Yuan period 元 (1279-1368). He came from Henei 河內 in the prefecture of Huaizhou 懷州 (modern Qinyang 沁陽, Henan),
During the disturbances of the Mongol conquest of the Jin empire 金 (1115-1234) in northern China his family fled to Xinzheng 新鄭 in modern Henan, then to Tai'an 泰安 in Shandong, and finally to Daming 大名 in Hebei. One year before the Jin fell Xu Heng was captured by the Mongols, but was allowed to take part in the state examinations, succeeded, and was made metropolitan superintendant of training (Jingzhao tixue 京兆提學) under the then-Prince Qubilai. When the latter made himself emperor of the Yuan dynasty Xu Heng was made Left Counsellor of the Imperial Secretariat (zhongshu zuocheng 中書左丞), then libationer (i.e. director, jijiu 祭酒) of the Directorate of Education (guozijian 國子學). In this position he had an important function in the organization of the state civil administration and the description of court rituals, and participated in the compilation of the national calendarShoushi li 授時歷.
In his philosophy Xu Heng stood under the influence of Neo-Confucianism in the teachings of the brother Cheng Hao 程顥 and Cheng Yi 程頤, and Zhu Xi 朱熹. They said that the "Way" (dao 道) was the basis of the universe. Xu Heng altered this strict view by the assumption that knowledge (zhi 知) and practice (xing 行) should be congruent, and that true knowledge was to be paired with energetic action (zhen zhi li xing 真知力行). In the question of nourishing virtue Xu Heng followed the Neo-Confucian ideas of maintaining respect (chijing 持敬), cherishing the nourishment of mind (cunyang 存養) and examining oneself (xingcha 省察).
Xu Heng's philosophy did not develop really new ideas, but he must be credited with spreading Neo-Confucian thought in northern China and so promoting the acceptance of this philosophy, and of Confucianism in general, by the Mongol rulers. Xu Heng suggested making Zhu Xi's commentaries to the Four Books, Sishu jizhu 四書集注, part of the curriculum for the preparation to the state examinations. He was therefore venerated as the "patriarch of Neo-Confucianism" (lixue zongshi 理學宗師) during the Yuan period.
Xu Heng's collected writings are called Luzhai yishu 魯齋遺書.